Background

This document has nls (non-linear least squares) regression fits to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass vs. stand age relationships. We calculated the biomass of each FIA plot by summing alive tree biomass (as reported by FIA). Stand age is also reported by FIA, using tree-core age estimates from two trees from the dominant size class of the FIA plot.

We considered the following Michaelis-Menten functional form \(B = (1 + (yr-1990)* ge/100) \times (1 - \alpha \cdot B_l) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac{A \cdot STDAGE_{t2}}{k+STDAGE_{t2}}\right)\), where \(B\) is the plot biomass, \(B_l\) is the calculated biomass loss (proportion) for the previous FIA plot census interval, \(STDAGE_{t2}\) is the stand age at the second of two FIA plot tree censuses, \(\Delta PDSI\) is the difference in the peak growing season (June-August) annual average PDSI values over the FIA plot measurement intervals and a 30-year climate normal (1960-1989), and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(ge\): biomass growth enhancement over time, \(A\): the Michaelis-Menten asymptote and \(k\): the Michaelis-Menten half-saturation constant.

Data have increasing variance in \(B\) with increasing \(STDAGE_{t2}\), thus, weighted-nls is the best approach. We explored a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {meanG}^2\) in equal-sample sized stand age bins (n=20 where possible, else n=10) for each ecoprovince. These bins are also used to visualize data means in relation to nls model fit.

Model selection is used to determine the best fitting models, which is implemented in three parts. The first part selected the best model form using \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest) and \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or the difference in the Palmer drought severity index from June - August for the 10 years preceding the biomass measurement and the 1960-1989 period).

model 1: simple model \(B = (1 + (yr-1990)* ge/100) \times \left( \frac {A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)

model 2: phi model \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac {A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)

model 3: phi-alpha model \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left( \frac {A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)

Then, model selection part two takes the best fitting model from part 1 and and adds the \(p\) and \(s\) parameters (individually then together) to modify the Micheaelis-Menten functional form. The \(p\) parameter allows for an intercept in the model (i.e., for the model to not be forced through the origin), and the \(s\) parameter increases model flexibility, with \(s\)>1 leading to more-sigmoidal shape.

sub-model a: p form \(pA + \left( \frac {(1-p) * A \cdot STDAGE_{t2}} {k+STDAGE_{t2}} \right)\)

sub-model b: s form \(\left( \frac {A \cdot STDAGE_{t2}^s} {k^s+STDAGE_{t2}^s} \right)\)

sub-model c: p and s together \(pA + \left( \frac {(1-p) *A \cdot STDAGE_{t2}^s} {k^s + STDAGE_{t1}^s} \right)\)

Lastly, model selection part 3, fits three similar models to model selection part one, but uses the Log-Normal functional form. The Log-Normal equation fits more of “hump-shaped” curve which allows for a decrease in biomass at old stand ages. Three Log-normal models are fitted: 1) the simple model, 2) the \(\phi\) model: accounting for climate variability (i.e., \(\Delta PDSI\)) and 3: the \(\phi\)-\(\alpha\) model: account for both climate variability and growth compensation due to plot biomass loss.

model 4: simple model \(B = (1 + (yr-1990)* ge/100) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(STDAGE_{t2} /c \right)} {d} \right]} ^2 \right)\)

model 5: phi model \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(STDAGE_{t2} /c \right)} {d} \right]} ^2 \right)\)

model 6: phi-alpha model \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(STDAGE_{t2} /c \right)} {d} \right]} ^2 \right)\)

Note:

This analysis only uses plot biomass data from the same plot locations and measurement intervals for which we also have data on biomass growth (which is used in the growth vs. biomass analysis ). We use the second of the two plot measurements comprising a \(G\) interval

This includes the following plot-based filtering criteria (which were used for the growth vs. biomass analysis):

  1. exclude FIA plots in plantation forests
  2. exclude FIA plots with multiple plot conditions (COND_PROP_UNADJ > 0.95)
  3. exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
  4. exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
  5. exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
  6. exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)

Below the model fitting procedure is implemented by ecoprovince:

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)    
## 1   6880     1758.3                              
## 2   6879     1757.8  1   0.555  2.1712 0.1407    
## 3   6826     1549.2 53 208.623 17.3444 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 74579.98
## 2     2 74579.81
## 3     3 73288.96
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      0.783844   0.191166   4.100 4.17e-05 ***
## phi    -0.006083   0.004050  -1.502    0.133    
## alpha   0.848174   0.027710  30.609  < 2e-16 ***
## A     387.282360  24.219054  15.991  < 2e-16 ***
## k     170.939329  11.561396  14.785  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4764 on 6826 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.994e-06
##   (53 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in Mod.Sel3 %in% c(1, "1a", "1b", "1c", 4) : 
##   object 'Mod.Sel3' not found
## Error in Mod.Sel3 %in% c(1, "1a", "1b", "1c", 4) : 
##   object 'Mod.Sel3' not found
## Error in Mod.Sel3 %in% c(1, "1a", "1b", "1c", 4) : 
##   object 'Mod.Sel3' not found
##   model      AIC
## 1     3 73288.96
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      0.783844   0.191166   4.100 4.17e-05 ***
## phi    -0.006083   0.004050  -1.502    0.133    
## alpha   0.848174   0.027710  30.609  < 2e-16 ***
## A     387.282360  24.219054  15.991  < 2e-16 ***
## k     170.939329  11.561396  14.785  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4764 on 6826 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.994e-06
##   (53 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   6878     1726.3                             
## 2   6877     1726.3  1   0.00   0.000 0.9999    
## 3   6824     1505.9 53 220.44  18.849 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 73288.96
## 2     4 74457.48
## 3     5 74459.48
## 4     6 73099.37
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    8.813e-01  1.963e-01   4.489 7.27e-06 ***
## phi   0.000e+00  4.073e-03   0.000        1    
## alpha 8.427e-01  2.665e-02  31.622  < 2e-16 ***
## a     3.796e+01  1.716e+00  22.121  < 2e-16 ***
## b     1.029e+02  4.675e+00  22.003  < 2e-16 ***
## c     1.147e+02  4.219e+00  27.183  < 2e-16 ***
## d     9.253e-01  3.938e-02  23.497  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4698 on 6824 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (53 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

predict and plot

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq   Df  Sum Sq F value Pr(>F)    
## 1  22648     8866.6                                
## 2  22642     8863.1    6    3.45  1.4684 0.1846    
## 3  18851     6790.9 3791 2072.26  1.5174 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 236627.9
## 2     2 236569.9
## 3     3 196512.3
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    2.912e-01  1.133e-01   2.570  0.01017 *  
## phi   7.851e-03  2.877e-03   2.729  0.00637 ** 
## alpha 7.062e-01  2.262e-02  31.215  < 2e-16 ***
## A     1.736e+02  4.978e+00  34.871  < 2e-16 ***
## k     6.414e+01  1.924e+00  33.330  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6002 on 18851 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 5.698e-07
##   (3829 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  18851     6790.9                                
## 2  18850     6692.5  1 98.406  277.17 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 196512.3
## 2    3a 196239.1
## 3    3b 196471.9
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    2.241e-01  1.093e-01   2.050  0.04040 *  
## phi   9.052e-03  2.859e-03   3.166  0.00155 ** 
## alpha 7.201e-01  1.902e-02  37.853  < 2e-16 ***
## A     2.301e+02  1.078e+01  21.336  < 2e-16 ***
## k     1.220e+02  8.649e+00  14.107  < 2e-16 ***
## p     4.587e-02  2.123e-03  21.611  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5959 on 18850 degrees of freedom
## 
## Number of iterations to convergence: 14 
## Achieved convergence tolerance: 7.141e-06
##   (3829 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq   Df  Sum Sq F value Pr(>F)    
## 1  22646     8719.0                                
## 2  22640     8716.1    6    2.81  1.2177 0.2935    
## 3  18849     6477.4 3791 2238.72  1.7184 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3a 196239.1
## 2     4 236251.5
## 3     5 236195.2
## 4     6 195625.2
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    4.140e-01  1.162e-01   3.563 0.000368 ***
## phi   7.961e-03  2.783e-03   2.860 0.004237 ** 
## alpha 7.834e-01  1.478e-02  52.994  < 2e-16 ***
## a     2.394e+01  6.952e-01  34.428  < 2e-16 ***
## b     8.032e+01  2.177e+00  36.900  < 2e-16 ***
## c     1.097e+02  2.987e+00  36.713  < 2e-16 ***
## d     1.196e+00  2.919e-02  40.962  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5862 on 18849 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3829 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

predict and plot

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)    
## 1   7303     1344.5                              
## 2   7302     1344.5  1   0.043  0.2328 0.6295    
## 3   7236     1180.4 66 164.021 15.2340 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 79950.98
## 2     2 79952.75
## 3     3 78504.02
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      0.150534   0.121581   1.238    0.216    
## phi    -0.002307   0.003371  -0.684    0.494    
## alpha   0.820917   0.026455  31.031   <2e-16 ***
## A     488.035490  25.376755  19.232   <2e-16 ***
## k     148.175964   8.787433  16.862   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4039 on 7236 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.121e-06
##   (66 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   7236     1180.4                           
## 2   7235     1180.4  1 0.072623  0.4451 0.5047
##   model      AIC
## 1     3 78504.02
## 2    3a 78505.57
## 3    3b 78486.11
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + 
##     STDAGE_t2^s))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      0.199221   0.124547   1.600    0.110    
## phi    -0.002882   0.003363  -0.857    0.392    
## alpha   0.828632   0.026693  31.043   <2e-16 ***
## A     328.159568  25.015982  13.118   <2e-16 ***
## k      75.605699   8.503967   8.891   <2e-16 ***
## s       1.204149   0.047079  25.577   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4034 on 7235 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 1.269e-06
##   (66 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   7301     1330.8                             
## 2   7300     1330.8  1   0.00   0.000      1    
## 3   7234     1163.2 66 167.61  15.794 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3b 78486.11
## 2     4 79879.95
## 3     5 79881.95
## 4     6 78401.23
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    1.821e-01  1.229e-01   1.482    0.138    
## phi   0.000e+00  3.355e-03   0.000    1.000    
## alpha 8.235e-01  2.507e-02  32.842   <2e-16 ***
## a     3.031e+01  2.059e+00  14.722   <2e-16 ***
## b     1.653e+02  7.505e+00  22.022   <2e-16 ***
## c     1.365e+02  9.187e+00  14.864   <2e-16 ***
## d     1.344e+00  6.315e-02  21.287   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.401 on 7234 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (66 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

predict and plot

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq   Df Sum Sq F value    Pr(>F)    
## 1   5841     1995.4                                  
## 2   5840     1991.5    1   3.94 11.5553 0.0006801 ***
## 3   4837     1493.8 1003 497.67  1.6066 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 62741.48
## 2     2 62731.93
## 3     3 51869.23
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.198275   0.190865  -1.039 0.298940    
## phi     0.026927   0.008166   3.298 0.000982 ***
## alpha   0.840626   0.041923  20.052  < 2e-16 ***
## A     433.451485  35.586083  12.180  < 2e-16 ***
## k     179.023537  16.475977  10.866  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5557 on 4837 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 5.237e-06
##   (1004 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   4837     1493.8                           
## 2   4836     1493.8  1 0.065605  0.2124 0.6449
##   model      AIC
## 1     3 51869.23
## 2    3a 51871.01
## 3    3b 51851.13
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + 
##     STDAGE_t2^s))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.142003   0.196013  -0.724 0.468819    
## phi     0.026869   0.008145   3.299 0.000978 ***
## alpha   0.861714   0.042348  20.348  < 2e-16 ***
## A     254.478620  25.639783   9.925  < 2e-16 ***
## k      74.310141  10.351858   7.178 8.12e-13 ***
## s       1.259046   0.060453  20.827  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5546 on 4836 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 4.249e-06
##   (1004 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq   Df Sum Sq F value    Pr(>F)    
## 1   5839     1955.8                                  
## 2   5838     1951.5    1   4.28 12.8130  0.000347 ***
## 3   4835     1439.8 1003 511.71  1.7132 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3b 51851.13
## 2     4 62628.31
## 3     5 62617.50
## 4     6 51694.96
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.160480   0.191030  -0.840 0.400905    
## phi     0.029310   0.008058   3.637 0.000279 ***
## alpha   0.861198   0.034858  24.706  < 2e-16 ***
## a      26.981910   1.590173  16.968  < 2e-16 ***
## b     117.431325   5.506609  21.326  < 2e-16 ***
## c     102.339914   4.395032  23.285  < 2e-16 ***
## d       1.016947   0.045310  22.444  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5457 on 4835 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1004 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

predict and plot

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq   Df Sum Sq F value    Pr(>F)    
## 1   9996     1894.8                                  
## 2   9995     1886.1    1   8.62 45.6873 1.465e-11 ***
## 3   8720     1565.2 1275 320.92  1.4023 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model       AIC
## 1     1 104296.40
## 2     2 104252.80
## 3     3  90827.83
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      0.396833   0.125814   3.154  0.00162 ** 
## phi    -0.024935   0.004067  -6.130 9.15e-10 ***
## alpha   0.760649   0.027047  28.124  < 2e-16 ***
## A     238.294969   8.772491  27.164  < 2e-16 ***
## k      71.732427   3.342762  21.459  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4237 on 8720 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 6.33e-06
##   (1281 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   8720     1565.2                          
## 2   8719     1565.0  1 0.16787  0.9352 0.3335
##   model      AIC
## 1     3 90827.83
## 2    3a 90828.90
## 3    3b 90795.04
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + 
##     STDAGE_t2^s))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      0.416271   0.126666   3.286  0.00102 ** 
## phi    -0.024882   0.004055  -6.136 8.81e-10 ***
## alpha   0.766041   0.027202  28.161  < 2e-16 ***
## A     173.765420   8.048890  21.589  < 2e-16 ***
## k      40.143985   2.546281  15.766  < 2e-16 ***
## s       1.357396   0.059895  22.663  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4229 on 8719 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.878e-06
##   (1281 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq   Df Sum Sq F value Pr(>F)    
## 1   9994     1868.9                               
## 2   9993     1868.9    1   0.00  0.0000      1    
## 3   8718     1536.5 1275 332.39  1.4792 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model       AIC
## 1    3b  90795.04
## 2     4 104162.96
## 3     5 104164.96
## 4     6  90670.25
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.11966    0.11180    1.07    0.285    
## phi     0.00000    0.00420    0.00    1.000    
## alpha   0.76968    0.02606   29.54   <2e-16 ***
## a      31.40349    1.94921   16.11   <2e-16 ***
## b     103.16963    3.49693   29.50   <2e-16 ***
## c     102.24775    4.00727   25.52   <2e-16 ***
## d       1.21270    0.05205   23.30   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4198 on 8718 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1281 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

predict and plot

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df Sum Sq F value Pr(>F)    
## 1  12796     4809.1                              
## 2  12795     4808.7   1   0.36  0.9571 0.3279    
## 3  12521     4175.2 274 633.57  6.9343 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 141420.6
## 2     2 141421.7
## 3     3 137622.5
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      1.298741   0.153046   8.486   <2e-16 ***
## phi    -0.004157   0.003895  -1.067    0.286    
## alpha   0.589610   0.018270  32.273   <2e-16 ***
## A     218.121169   7.367848  29.604   <2e-16 ***
## k      49.029679   1.573432  31.161   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5775 on 12521 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.048e-06
##   (318 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_231,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  12521     4175.2                                
## 2  12520     3964.7  1 210.43  664.52 < 2.2e-16 ***
## 3  12519     3859.6  1 105.14  341.03 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 137622.5
## 2    3a 136976.7
## 3    3b       NA
## 4    3c 136642.1
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      2.217572   0.194135  11.423   <2e-16 ***
## phi    -0.004290   0.003665  -1.171    0.242    
## alpha   0.806123   0.010262  78.552   <2e-16 ***
## A     126.582471   4.627536  27.354   <2e-16 ***
## k      32.083156   0.874214  36.699   <2e-16 ***
## p       0.201159   0.007276  27.645   <2e-16 ***
## s       2.406768   0.105540  22.804   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5552 on 12519 degrees of freedom
## 
## Number of iterations to convergence: 16 
## Achieved convergence tolerance: 8.359e-06
##   (318 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value Pr(>F)    
## 1  12794     4770.2                              
## 2  12793     4770.2   1    0.0   0.000 0.9999    
## 3  12519     3858.0 274  912.2  10.803 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3c 136642.1
## 2     4 141320.7
## 3     5 141322.7
## 4     6 136636.9
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    2.122e+00  1.886e-01   11.25   <2e-16 ***
## phi   0.000e+00  3.654e-03    0.00        1    
## alpha 8.066e-01  1.021e-02   79.00   <2e-16 ***
## a     2.610e+01  7.952e-01   32.82   <2e-16 ***
## b     9.784e+01  3.899e+00   25.10   <2e-16 ***
## c     1.017e+02  5.567e+00   18.27   <2e-16 ***
## d     1.383e+00  4.701e-02   29.43   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5551 on 12519 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (318 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

predict and plot

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1  13052     7462.8                                 
## 2  13051     7457.1   1   5.67  9.9174  0.001641 ** 
## 3  12737     6769.2 314 687.93  4.1223 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 146999.4
## 2     2 146991.5
## 3     3 143242.9
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    8.326e-01  1.651e-01   5.042 4.67e-07 ***
## phi   1.285e-02  4.608e-03   2.789   0.0053 ** 
## alpha 6.349e-01  1.913e-02  33.183  < 2e-16 ***
## A     2.157e+02  8.767e+00  24.605  < 2e-16 ***
## k     4.550e+01  1.798e+00  25.310  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.729 on 12737 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.205e-06
##   (425 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_232,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_232,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1  12737     6769.2                                
## 2  12736     6281.7  1 487.49  988.38 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 143242.9
## 2    3a 142292.6
## 3    3b       NA
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    1.282e+00  1.808e-01   7.093 1.38e-12 ***
## phi   2.125e-02  4.315e-03   4.924 8.59e-07 ***
## alpha 8.382e-01  9.762e-03  85.865  < 2e-16 ***
## A     6.850e+02  1.294e+02   5.296 1.20e-07 ***
## k     3.849e+02  8.839e+01   4.354 1.34e-05 ***
## p     3.517e-02  5.927e-03   5.935 3.01e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7023 on 12736 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 8.658e-06
##   (425 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df  Sum Sq F value    Pr(>F)    
## 1  13050     7396.2                                  
## 2  13049     7390.0   1    6.16 10.8706 0.0009796 ***
## 3  12735     6114.6 314 1275.39  8.4595 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3a 142292.6
## 2     4 146886.4
## 3     5 146877.5
## 4     6 141951.1
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    1.323e+00  1.792e-01   7.379 1.69e-13 ***
## phi   2.238e-02  4.214e-03   5.312 1.10e-07 ***
## alpha 8.716e-01  8.279e-03 105.282  < 2e-16 ***
## a     3.279e+01  1.074e+00  30.514  < 2e-16 ***
## b     1.046e+02  4.797e+00  21.803  < 2e-16 ***
## c     1.062e+02  6.936e+00  15.316  < 2e-16 ***
## d     1.323e+00  5.441e-02  24.316  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6929 on 12735 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (425 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

predict and plot

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)    
## 1   1339     479.03                              
## 2   1338     477.61  1   1.417  3.9708 0.0465 *  
## 3   1277     328.24 61 149.369  9.5264 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 15098.92
## 2     2 15096.94
## 3     3 14148.33
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.05537    0.41382   0.134    0.894    
## phi     0.02170    0.01451   1.496    0.135    
## alpha   0.66209    0.05415  12.226  < 2e-16 ***
## A     550.84136   93.74731   5.876 5.36e-09 ***
## k     164.62568   31.36459   5.249 1.79e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.507 on 1277 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.843e-06
##   (62 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_234,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   1277     328.24                           
## 2   1276     328.19  1 0.044987  0.1749 0.6759
##   model      AIC
## 1     3 14148.33
## 2    3a 14150.15
## 3    3b 14149.70
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.05537    0.41382   0.134    0.894    
## phi     0.02170    0.01451   1.496    0.135    
## alpha   0.66209    0.05415  12.226  < 2e-16 ***
## A     550.84136   93.74731   5.876 5.36e-09 ***
## k     164.62568   31.36459   5.249 1.79e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.507 on 1277 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.843e-06
##   (62 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Error in nls(f_5, data = G_234, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: singular convergence (7)
## Error in nls(f_6, data = G_234, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
##   model      AIC
## 1     3 14148.33
## 2     4 15100.79
## 3     5       NA
## 4     6       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.05537    0.41382   0.134    0.894    
## phi     0.02170    0.01451   1.496    0.135    
## alpha   0.66209    0.05415  12.226  < 2e-16 ***
## A     550.84136   93.74731   5.876 5.36e-09 ***
## k     164.62568   31.36459   5.249 1.79e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.507 on 1277 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.843e-06
##   (62 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95697, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -11.379, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df  Sum Sq F value Pr(>F)    
## 1   2284     617.34                               
## 2   2283     617.31   1   0.034  0.1246 0.7241    
## 3   1779     393.26 504 224.054  2.0110 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 24037.04
## 2     2 24038.91
## 3     3 18554.02
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      0.452101   0.337258   1.341    0.180    
## phi    -0.009728   0.008348  -1.165    0.244    
## alpha   0.723061   0.066976  10.796   <2e-16 ***
## A     253.307381  25.881776   9.787   <2e-16 ***
## k     100.370377  11.700089   8.579   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4702 on 1779 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.02e-06
##   (506 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1   1779     393.26                           
## 2   1778     393.16  1 0.099492  0.4499 0.5025
##   model      AIC
## 1     3 18554.02
## 2    3a 18555.57
## 3    3b 18535.55
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + 
##     STDAGE_t2^s))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      0.461374   0.337089   1.369    0.171    
## phi    -0.007587   0.008354  -0.908    0.364    
## alpha   0.734801   0.067811  10.836   <2e-16 ***
## A     145.037642  13.621784  10.647   <2e-16 ***
## k      38.922297   3.519170  11.060   <2e-16 ***
## s       1.702253   0.153066  11.121   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4676 on 1778 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 9.034e-06
##   (506 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value Pr(>F)    
## 1   2282     595.32                              
## 2   2281     595.32   1   0.00  0.0000      1    
## 3   1777     380.67 504 214.65  1.9881 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3b 18535.55
## 2     4 23957.97
## 3     5 23959.97
## 4     6 18500.01
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.316611   0.315076   1.005    0.315    
## phi    0.000000   0.008366   0.000    1.000    
## alpha  0.721003   0.065836  10.952  < 2e-16 ***
## a     26.749847   3.883232   6.889  7.8e-12 ***
## b     93.309963   7.589862  12.294  < 2e-16 ***
## c     99.589633   6.919253  14.393  < 2e-16 ***
## d      1.097516   0.093714  11.711  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4628 on 1777 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (506 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9672, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -18.437, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1    708     336.70                             
## 2    707     336.59  1  0.114  0.2387 0.6253    
## 3    663     256.40 44 80.193  4.7129 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7311.058
## 2     2 7312.818
## 3     3 6847.424
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.11049    0.45757  -0.241    0.809    
## phi    -0.01619    0.01548  -1.046    0.296    
## alpha   0.58972    0.09275   6.358 3.81e-10 ***
## A     194.05332   30.30528   6.403 2.88e-10 ***
## k      60.73530   10.48651   5.792 1.08e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6219 on 663 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.75e-06
##   (46 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    663      256.4                              
## 2    662      253.4  1 2.9955  7.8256 0.005301 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 6847.424
## 2    3a 6841.574
## 3    3b 6848.960
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.015226   0.475959  -0.032  0.97449    
## phi    -0.015314   0.015369  -0.996  0.31943    
## alpha   0.598558   0.086108   6.951 8.69e-12 ***
## A     266.510967  86.162862   3.093  0.00206 ** 
## k     119.972028  58.508932   2.050  0.04071 *  
## p       0.032368   0.008238   3.929 9.42e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6187 on 662 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 9.122e-06
##   (46 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1    706     321.06                             
## 2    705     320.94  1  0.124  0.2721 0.6021    
## 3    661     239.34 44 81.603  5.1221 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3a 6841.574
## 2     4 7281.242
## 3     5 7282.967
## 4     6 6805.432
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.18595    0.42015  -0.443    0.658    
## phi    0.00000    0.01468   0.000    1.000    
## alpha  0.64304    0.07775   8.271 7.33e-16 ***
## a     22.55849    2.85029   7.914 1.05e-14 ***
## b     75.97870    8.55425   8.882  < 2e-16 ***
## c     59.50946    5.45495  10.909  < 2e-16 ***
## d      0.99855    0.11455   8.717  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6017 on 661 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (46 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93637, p-value = 2.822e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -9.5618, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • unable to fit model (only 64 observations)

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

262 - California Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • unable to fit model (0 observations)

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)  
## 1    155     28.883                             
## 2    154     28.876  1 0.00774  0.0413 0.83924  
## 3    150     26.624  4 2.25207  3.1721 0.01552 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 1995.769
## 2     2 1997.727
## 3     3 1954.695
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)   
## ge      -0.20199    1.19725  -0.169  0.86625   
## phi     -0.05404    0.06721  -0.804  0.42264   
## alpha    0.75695    0.24731   3.061  0.00262 **
## A     6638.54989 2801.18595   2.370  0.01906 * 
## k     1264.32167  414.66988   3.049  0.00271 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4213 on 150 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 6.736e-06
##   (4 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_263,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_263,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)  
## 1    150     26.624                            
## 2    149     25.750  1 0.87387  5.0566  0.026 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 1954.695
## 2    3a 1951.522
## 3    3b       NA
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge    -7.777e-02  1.282e+00  -0.061 0.951698    
## phi   -2.712e-02  6.706e-02  -0.404 0.686456    
## alpha  8.593e-01  2.401e-01   3.579 0.000466 ***
## A      1.932e+04  2.056e+04   0.940 0.348869    
## k      4.916e+03  5.597e+03   0.878 0.381211    
## p      3.006e-03  2.553e-03   1.178 0.240857    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4157 on 149 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 5.081e-06
##   (4 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    153     30.979                            
## 2    152     30.979  1 0.0000  0.0000 1.00000  
## 3    148     28.736  4 2.2433  2.8885 0.02441 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3a 1951.522
## 2     4 2010.835
## 3     5 2012.835
## 4     6 1970.528
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge    -7.777e-02  1.282e+00  -0.061 0.951698    
## phi   -2.712e-02  6.706e-02  -0.404 0.686456    
## alpha  8.593e-01  2.401e-01   3.579 0.000466 ***
## A      1.932e+04  2.056e+04   0.940 0.348869    
## k      4.916e+03  5.597e+03   0.878 0.381211    
## p      3.006e-03  2.553e-03   1.178 0.240857    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4157 on 149 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 5.081e-06
##   (4 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94451, p-value = 8.565e-06
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.165, p-value = 0.03038
## alternative hypothesis: two.sided

predict and plot

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    214     67.657                          
## 2    213     67.601  1 0.05588  0.1761 0.6752
## 3    210     67.034  3 0.56784  0.5930 0.6203
##   model      AIC
## 1     1 2322.942
## 2     2 2324.763
## 3     3 2310.678
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)  
## ge     -0.75338    0.99763  -0.755   0.4510  
## phi     0.01946    0.03797   0.512   0.6089  
## alpha  -0.08479    0.30668  -0.276   0.7825  
## A     258.05809  102.79459   2.510   0.0128 *
## k     135.22109   55.86986   2.420   0.0164 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.565 on 210 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 5.081e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df    Sum Sq F value Pr(>F)
## 1    210     67.034                            
## 2    209     67.029  1 0.0047244  0.0147 0.9035
##   model      AIC
## 1     3 2310.678
## 2    3a 2312.663
## 3    3b 2311.948
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)  
## ge     -0.75338    0.99763  -0.755   0.4510  
## phi     0.01946    0.03797   0.512   0.6089  
## alpha  -0.08479    0.30668  -0.276   0.7825  
## A     258.05809  102.79459   2.510   0.0128 *
## k     135.22109   55.86986   2.420   0.0164 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.565 on 210 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 5.081e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    212     62.692                          
## 2    211     62.495  1 0.19729  0.6661 0.4153
## 3    208     60.709  3 1.78543  2.0391 0.1095
##   model      AIC
## 1     3 2310.678
## 2     4 2310.402
## 3     5 2311.718
## 4     6 2293.372
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.28713    0.67518  -1.906 0.057982 .  
## phi     0.03227    0.03517   0.918 0.359882    
## alpha   0.29974    0.24631   1.217 0.225013    
## a      53.32207   16.30891   3.270 0.001261 ** 
## b     144.62680   42.16073   3.430 0.000727 ***
## c     139.92344    7.50050  18.655  < 2e-16 ***
## d       0.57294    0.08596   6.665 2.33e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5403 on 208 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91535, p-value = 9.76e-10
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.201, p-value = 0.2297
## alternative hypothesis: two.sided

predict and plot

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

322 - American Semidesert and Desert

model selection 1

## Error in nls(f_1, data = G_322, start = c(ge = ge.start, A = A.start,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_322$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_322.", Mod.Sel1, sep = "")) : 
##   object 'nls_322.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"
  • Cannot fit model
  • not enough data (only 3 observations)

331 - Great Plains/Palouse Dry Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1    327     230.98                                 
## 2    326     221.26  1  9.7243 14.3276 0.0001828 ***
## 3    308     205.48 18 15.7769  1.3138 0.1767975    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3395.864
## 2     2 3383.670
## 3     3 3221.135
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     4.26044    5.00230   0.852  0.39504    
## phi   -0.09420    0.02031  -4.638 5.20e-06 ***
## alpha  0.71650    0.17048   4.203 3.46e-05 ***
## A     38.23376   22.39968   1.707  0.08885 .  
## k     18.37690    5.72664   3.209  0.00147 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8168 on 308 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 3.76e-06
##   (18 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_331,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    308     205.48                                
## 2    307     196.58  1 8.9062  13.909 0.0002285 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 3221.135
## 2    3a 3209.266
## 3    3b       NA
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.72254    1.74633   0.414  0.67935    
## phi    -0.08876    0.02070  -4.288 2.42e-05 ***
## alpha   0.85825    0.11815   7.264 3.11e-12 ***
## A     100.86242   65.16488   1.548  0.12270    
## k     119.62952  132.17299   0.905  0.36612    
## p       0.19994    0.07696   2.598  0.00983 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8002 on 307 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 9.255e-06
##   (18 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Error in nls(f_6, data = G_331, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df     Sum Sq F value Pr(>F)
## 1    325     228.37                             
## 2    324     228.37  1 2.1774e-06       0 0.9986
##   model      AIC
## 1    3a 3209.266
## 2     4 3396.105
## 3     5 3398.105
## 4     6       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.72254    1.74633   0.414  0.67935    
## phi    -0.08876    0.02070  -4.288 2.42e-05 ***
## alpha   0.85825    0.11815   7.264 3.11e-12 ***
## A     100.86242   65.16488   1.548  0.12270    
## k     119.62952  132.17299   0.905  0.36612    
## p       0.19994    0.07696   2.598  0.00983 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8002 on 307 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 9.255e-06
##   (18 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90048, p-value = 1.769e-13
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.7492, p-value = 8.966e-09
## alternative hypothesis: two.sided

predict and plot

plotting 2

* Cannot fit model

332 - Great Plains Steppe

model selection 1

## Error in nls(f_1, data = G_332, start = c(ge = ge.start, A = A.start,  : 
##   singular gradient
## Error in nls(f_2, data = G_332, start = c(ge = ge.start, phi = phi.start,  : 
##   singular gradient
##   model      AIC
## 1     1       NA
## 2     2       NA
## 3     3 2128.795
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)   
## ge      1.02847    2.21721   0.464  0.64328   
## phi    -0.01127    0.03204  -0.352  0.72537   
## alpha   0.80688    0.30138   2.677  0.00807 **
## A     385.25740  387.86420   0.993  0.32183   
## k     276.62580  301.37090   0.918  0.35983   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8067 on 191 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.576e-06
##   (36 observations deleted due to missingness)

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "a", sep = "")), data = G_332,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_332,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     3 2128.795
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)   
## ge      1.02847    2.21721   0.464  0.64328   
## phi    -0.01127    0.03204  -0.352  0.72537   
## alpha   0.80688    0.30138   2.677  0.00807 **
## A     385.25740  387.86420   0.993  0.32183   
## k     276.62580  301.37090   0.918  0.35983   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8067 on 191 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.576e-06
##   (36 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    225     139.58                         
## 2    224     139.58  1  0.000  0.0000 1.0000
## 3    189     115.51 35 24.075  1.1255 0.3019
##   model      AIC
## 1     3 2128.795
## 2     4 2445.978
## 3     5 2447.978
## 4     6 2118.424
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      1.18136    2.27869   0.518  0.60476    
## phi     0.00000    0.03192   0.000  1.00000    
## alpha   0.81823    0.23985   3.411  0.00079 ***
## a      25.78527   12.60017   2.046  0.04210 *  
## b      77.36146   65.72373   1.177  0.24065    
## c     143.44351  153.97937   0.932  0.35274    
## d       1.08261    0.74704   1.449  0.14894    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7818 on 189 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (36 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.88018, p-value = 2.243e-11
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.5496, p-value = 2.864e-08
## alternative hypothesis: two.sided

predict and plot

plotting 2

341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"
  • model not fitted because only 62 observations

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

342 - Intermountain Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

## [1] "cannot plot observed vs. predicted"

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   6772     1333.1                                 
## 2   6771     1327.8  1   5.352  27.294 1.799e-07 ***
## 3   6747     1121.9 24 205.845  51.580 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 71776.53
## 2     2 71751.27
## 3     3 70444.76
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    7.378e-01  1.631e-01   4.523 6.21e-06 ***
## phi   1.749e-02  3.545e-03   4.933 8.29e-07 ***
## alpha 8.125e-01  2.205e-02  36.852  < 2e-16 ***
## A     3.887e+02  2.185e+01  17.789  < 2e-16 ***
## k     1.763e+02  1.000e+01  17.626  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4078 on 6747 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 6.706e-06
##   (26 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6747     1121.9                                
## 2   6746     1117.8  1 4.1104  24.807 6.495e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 70444.76
## 2    3a 70421.98
## 3    3b 70407.65
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + 
##     STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    6.537e-01  1.575e-01   4.150 3.37e-05 ***
## phi   1.621e-02  3.525e-03   4.599 4.33e-06 ***
## alpha 8.187e-01  2.218e-02  36.910  < 2e-16 ***
## A     2.377e+02  1.599e+01  14.864  < 2e-16 ***
## k     7.376e+01  7.108e+00  10.377  < 2e-16 ***
## s     1.275e+00  4.822e-02  26.448  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4066 on 6746 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 3.339e-06
##   (26 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   6770     1322.9                                 
## 2   6769     1318.2  1   4.706  24.168 9.038e-07 ***
## 3   6745     1113.3 24 204.935  51.735 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3b 70407.65
## 2     4 71728.53
## 3     5 71706.38
## 4     6 70396.58
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    6.752e-01  1.589e-01   4.249 2.18e-05 ***
## phi   1.618e-02  3.519e-03   4.598 4.34e-06 ***
## alpha 8.210e-01  2.190e-02  37.487  < 2e-16 ***
## a     1.653e+01  2.717e+00   6.084 1.24e-09 ***
## b     1.482e+02  1.019e+01  14.549  < 2e-16 ***
## c     1.995e+02  2.424e+01   8.228 2.27e-16 ***
## d     1.645e+00  1.086e-01  15.152  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4063 on 6745 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (26 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

predict and plot

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   8180     1388.9                                 
## 2   8179     1375.5  1  13.387  79.603 < 2.2e-16 ***
## 3   8123     1262.9 56 112.597  12.933 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 90550.28
## 2     2 90473.02
## 3     3 89329.70
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      1.175313   0.144300   8.145 4.36e-16 ***
## phi    -0.031966   0.003502  -9.127  < 2e-16 ***
## alpha   0.842348   0.033283  25.309  < 2e-16 ***
## A     239.152856   7.892077  30.303  < 2e-16 ***
## k      57.456845   2.250413  25.532  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3943 on 8123 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 2.2e-06
##   (58 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df Sum Sq  F value Pr(>F)    
## 1   8123     1262.9                              
## 2   8122     1262.9  1  0.006   0.0363 0.8489    
## 3   8122     1256.5  0  0.000                    
## 4   8121     1224.6  1 31.907 211.5962 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 89329.70
## 2    3a 89331.66
## 3    3b 89290.55
## 4    3c 89083.49
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      1.357729   0.151543   8.959   <2e-16 ***
## phi    -0.031471   0.003435  -9.163   <2e-16 ***
## alpha   0.845265   0.029911  28.259   <2e-16 ***
## A     148.489315   4.499786  32.999   <2e-16 ***
## k      38.361942   0.798390  48.049   <2e-16 ***
## p       0.254305   0.013146  19.345   <2e-16 ***
## s       2.978640   0.176324  16.893   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3883 on 8121 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 3.624e-06
##   (58 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   8178     1358.7                             
## 2   8177     1358.7  1   0.00   0.000      1    
## 3   8121     1234.5 56 124.24  14.595 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3c 89083.49
## 2     4 90374.77
## 3     5 90376.77
## 4     6 89148.89
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      1.357729   0.151543   8.959   <2e-16 ***
## phi    -0.031471   0.003435  -9.163   <2e-16 ***
## alpha   0.845265   0.029911  28.259   <2e-16 ***
## A     148.489315   4.499786  32.999   <2e-16 ***
## k      38.361942   0.798390  48.049   <2e-16 ***
## p       0.254305   0.013146  19.345   <2e-16 ***
## s       2.978640   0.176324  16.893   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3883 on 8121 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 3.624e-06
##   (58 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

predict and plot

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1    887     122.26                                 
## 2    886     119.04  1  3.2238  23.995 1.148e-06 ***
## 3    881     103.70  5 15.3390  26.064 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 9055.244
## 2     2 9033.461
## 3     3 8884.472
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.48170    0.22025  -2.187    0.029 *  
## phi     0.05665    0.01331   4.255 2.32e-05 ***
## alpha   0.88034    0.07223  12.188  < 2e-16 ***
## A     307.38272   34.06829   9.023  < 2e-16 ***
## k      92.08986   14.22329   6.475 1.58e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3431 on 881 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 6.302e-07
##   (7 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M223,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    881      103.7                          
## 2    880      103.5  1 0.19217  1.6338 0.2015
##   model      AIC
## 1     3 8884.472
## 2    3a 8884.828
## 3    3b 8886.130
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.48170    0.22025  -2.187    0.029 *  
## phi     0.05665    0.01331   4.255 2.32e-05 ***
## alpha   0.88034    0.07223  12.188  < 2e-16 ***
## A     307.38272   34.06829   9.023  < 2e-16 ***
## k      92.08986   14.22329   6.475 1.58e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3431 on 881 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 6.302e-07
##   (7 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1    885     121.92                                 
## 2    884     118.67  1  3.2543  24.242 1.014e-06 ***
## 3    879     103.55  5 15.1183  25.667 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 8884.472
## 2     4 9056.791
## 3     5 9034.713
## 4     6 8887.220
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.48170    0.22025  -2.187    0.029 *  
## phi     0.05665    0.01331   4.255 2.32e-05 ***
## alpha   0.88034    0.07223  12.188  < 2e-16 ***
## A     307.38272   34.06829   9.023  < 2e-16 ***
## k      92.08986   14.22329   6.475 1.58e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3431 on 881 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 6.302e-07
##   (7 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96281, p-value = 3.117e-14
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -13.76, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)    
## 1   1005     242.87                              
## 2   1004     242.30  1  0.5714  2.3678 0.1242    
## 3    990     213.67 14 28.6282  9.4747 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 10414.94
## 2     2 10414.56
## 3     3 10207.82
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    6.345e-01  5.315e-01   1.194    0.233    
## phi   3.774e-03  1.472e-02   0.256    0.798    
## alpha 7.252e-01  6.819e-02  10.636  < 2e-16 ***
## A     2.251e+02  3.098e+01   7.267 7.46e-13 ***
## k     8.717e+01  1.169e+01   7.459 1.91e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4646 on 990 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.806e-06
##   (14 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value   Pr(>F)   
## 1    990     213.67                               
## 2    989     212.14  1 1.52740  7.1208 0.007744 **
## 3    989     212.14  0 0.00000                    
## 4    988     212.12  1 0.02084  0.0971 0.755417   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 10207.82
## 2    3a 10202.68
## 3    3b 10202.66
## 4    3c 10204.57
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + 
##     STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    5.442e-01  5.113e-01   1.064    0.287    
## phi   3.429e-03  1.470e-02   0.233    0.816    
## alpha 7.388e-01  6.391e-02  11.561  < 2e-16 ***
## A     6.025e+03  8.360e+04   0.072    0.943    
## k     2.222e+04  4.647e+05   0.048    0.962    
## s     7.043e-01  1.107e-01   6.363 3.02e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4631 on 989 degrees of freedom
## 
## Number of iterations to convergence: 16 
## Achieved convergence tolerance: 4.751e-06
##   (14 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Error in nls(f_6, data = G_M231, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   1003     242.05                          
## 2   1002     241.48  1 0.57363  2.3802 0.1232
##   model      AIC
## 1    3b 10202.66
## 2     4 10415.55
## 3     5 10415.16
## 4     6       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + 
##     STDAGE_t2^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    5.442e-01  5.113e-01   1.064    0.287    
## phi   3.429e-03  1.470e-02   0.233    0.816    
## alpha 7.388e-01  6.391e-02  11.561  < 2e-16 ***
## A     6.025e+03  8.360e+04   0.072    0.943    
## k     2.222e+04  4.647e+05   0.048    0.962    
## s     7.043e-01  1.107e-01   6.363 3.02e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4631 on 989 degrees of freedom
## 
## Number of iterations to convergence: 16 
## Achieved convergence tolerance: 4.751e-06
##   (14 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96071, p-value = 1.042e-15
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -13.329, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M242 - Cascade Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)    
## 1   3298     2133.7                              
## 2   3297     2133.5  1   0.185  0.2856 0.5931    
## 3   3223     1973.9 74 159.675  3.5233 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 43707.67
## 2     2 43709.38
## 3     3 42726.34
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge    -3.865e-01  4.503e-01  -0.858    0.391    
## phi    7.455e-03  1.536e-02   0.485    0.627    
## alpha  1.048e+00  6.743e-02  15.534  < 2e-16 ***
## A      1.204e+03  1.796e+02   6.702 2.41e-11 ***
## k      3.384e+02  3.148e+01  10.750  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7826 on 3223 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 2.764e-06
##   (75 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   3223     1973.9                                
## 2   3222     1944.4  1 29.448  48.796 3.435e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 42726.34
## 2    3a 42679.82
## 3    3b       NA
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.286311   0.468612  -0.611    0.541    
## phi     0.001043   0.015220   0.069    0.945    
## alpha   1.094399   0.065937  16.598  < 2e-16 ***
## A     886.863086 131.191842   6.760 1.63e-11 ***
## k     183.453925  21.899737   8.377  < 2e-16 ***
## p      -0.050509   0.011006  -4.589 4.62e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7768 on 3222 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 5.33e-06
##   (75 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   3296     2088.0                             
## 2   3295     2088.0  1   0.00  0.0000      1    
## 3   3221     1937.6 74 150.37  3.3781 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3a 42679.82
## 2     4 43640.14
## 3     5 43642.14
## 4     6 42670.50
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.27245    0.47058  -0.579    0.563    
## phi     0.00000    0.01519   0.000    1.000    
## alpha   1.08485    0.06785  15.990  < 2e-16 ***
## a       8.65674   10.66920   0.811    0.417    
## b     568.18302   85.65471   6.633 3.83e-11 ***
## c     556.00850  107.68623   5.163 2.57e-07 ***
## d       2.03645    0.16934  12.026  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7756 on 3221 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (75 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94604, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -16.722, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq  Df  Sum Sq  F value Pr(>F)    
## 1   1983    1184.82                                
## 2   1982    1086.49   1  98.334 179.3835 <2e-16 ***
## 3   1698     969.05 284 117.440   0.7246 0.9997    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 24895.19
## 2     2 24725.12
## 3     3 21327.35
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.15844    0.33074  -3.503 0.000473 ***
## phi     0.20254    0.01308  15.487  < 2e-16 ***
## alpha   0.75554    0.10170   7.429 1.72e-13 ***
## A     858.62930  116.97742   7.340 3.29e-13 ***
## k     131.30793   16.80895   7.812 9.80e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7554 on 1698 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 4.086e-07
##   (290 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1   1698     969.05                          
## 2   1697     968.64  1 0.40720  0.7134 0.3984
## 3   1697     968.83  0 0.00000               
## 4   1696     968.60  1 0.23227  0.4067 0.5237
##   model      AIC
## 1     3 21327.35
## 2    3a 21328.64
## 3    3b 21328.98
## 4    3c 21330.57
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.15844    0.33074  -3.503 0.000473 ***
## phi     0.20254    0.01308  15.487  < 2e-16 ***
## alpha   0.75554    0.10170   7.429 1.72e-13 ***
## A     858.62930  116.97742   7.340 3.29e-13 ***
## k     131.30793   16.80895   7.812 9.80e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7554 on 1698 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 4.086e-07
##   (290 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq  F value Pr(>F)    
## 1   1981    1183.63                               
## 2   1980    1084.37   1  99.26 181.2432 <2e-16 ***
## 3   1696     968.78 284 115.59   0.7125 0.9998    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 21327.35
## 2     4 24897.19
## 3     5 24725.25
## 4     6 21330.89
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.15844    0.33074  -3.503 0.000473 ***
## phi     0.20254    0.01308  15.487  < 2e-16 ***
## alpha   0.75554    0.10170   7.429 1.72e-13 ***
## A     858.62930  116.97742   7.340 3.29e-13 ***
## k     131.30793   16.80895   7.812 9.80e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7554 on 1698 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 4.086e-07
##   (290 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89658, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.3916, p-value = 1.125e-05
## alternative hypothesis: two.sided

predict and plot

plotting 2

M262 - California coastal range - coniferous forest - open woodland - shrub meadow

Model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

summary

  • simple log-normal model: does not fit
  • log-normal phi model: does not fit
  • log-normal phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"
  • model can fit - but K is negative (only 19 observations) - model excluded

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    363     122.71                              
## 2    362     120.40  1 2.3108  6.9479 0.008753 **
## 3    360     116.95  2 3.4501  5.3102 0.005336 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3833.912
## 2     2 3828.954
## 3     3 3813.507
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.79971    0.34921  -5.154 4.22e-07 ***
## phi     0.05202    0.02186   2.379  0.01786 *  
## alpha   0.51051    0.14684   3.477  0.00057 ***
## A     571.89280  200.04822   2.859  0.00450 ** 
## k     207.88399   95.57943   2.175  0.03028 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.57 on 360 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 4.209e-06
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("f_", Mod.Sel1, "b", sep = "")), data = G_M313,  : 
##   number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    360     116.95                            
## 2    359     115.13  1 1.8152  5.6599 0.01788 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 3813.507
## 2    3a 3809.797
## 3    3b       NA
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge      -1.81719    0.33976  -5.349 1.58e-07 ***
## phi      0.05053    0.02187   2.310   0.0215 *  
## alpha    0.55632    0.13755   4.045 6.42e-05 ***
## A     1053.49011  935.16228   1.127   0.2607    
## k      553.32368  612.06966   0.904   0.3666    
## p        0.02699    0.01970   1.370   0.1717    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5663 on 359 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 8.769e-06
##   (2 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    361     120.72                                
## 2    360     118.33  1 2.3867  7.2613 0.0073760 ** 
## 3    358     113.12  2 5.2114  8.2467 0.0003152 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3a 3809.797
## 2     4 3831.912
## 3     5 3826.603
## 4     6 3805.346
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.64684    0.39761  -4.142 4.30e-05 ***
## phi     0.04942    0.02191   2.255 0.024706 *  
## alpha   0.58276    0.13139   4.435 1.23e-05 ***
## a      49.30946   12.91826   3.817 0.000159 ***
## b     182.53573   43.85848   4.162 3.96e-05 ***
## c     174.61256   38.10635   4.582 6.36e-06 ***
## d       0.95327    0.19974   4.773 2.65e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5621 on 358 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9444, p-value = 1.805e-10
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 0.0034951, p-value = 0.9972
## alternative hypothesis: two.sided

predict and plot

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   1736     651.22                             
## 2   1735     650.35  1  0.875  2.3355 0.1266    
## 3   1713     585.52 22 64.825  8.6205 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 18138.23
## 2     2 18137.89
## 3     3 17801.62
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.86844    0.34495  -2.518   0.0119 *  
## phi     0.02219    0.01101   2.014   0.0441 *  
## alpha   0.61462    0.04179  14.707  < 2e-16 ***
## A     264.86669   35.08407   7.549 7.06e-14 ***
## k     114.94824   11.56820   9.937  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5846 on 1713 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 2.39e-06
##   (39 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Warning in nls(get(paste("f_", Mod.Sel1, "c", sep = "")), data = G_M331, : No starting values specified for some parameters.
## Initializing 'ge', 'phi', 'p', 'A', 's', 'k' to '1.'.
## Consider specifying 'start' or using a selfStart model
## Error in model.frame.default(formula = ~B_plt_t2_MgHa + MEASTIME_t2 +  : 
##   variable lengths differ (found for '(sstart)')
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1713     585.52                                
## 2   1712     579.19  1 6.3281  18.705 1.614e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 17801.62
## 2    3a 17784.95
## 3    3b 17795.30
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.841945   0.348432  -2.416   0.0158 *  
## phi     0.022076   0.010982   2.010   0.0446 *  
## alpha   0.629831   0.039965  15.760  < 2e-16 ***
## A     338.896959  58.574560   5.786 8.57e-09 ***
## k     209.274046  46.773721   4.474 8.18e-06 ***
## p       0.043809   0.007593   5.770 9.40e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5816 on 1712 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 5.915e-06
##   (39 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)    
## 1   1734     645.18                              
## 2   1733     644.14  1  1.038  2.7914 0.09495 .  
## 3   1711     571.23 22 72.908  9.9264 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3a 17784.95
## 2     4 18126.02
## 3     5 18125.22
## 4     6 17763.18
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.88397    0.33594  -2.631  0.00858 ** 
## phi     0.02721    0.01079   2.523  0.01174 *  
## alpha   0.64195    0.03893  16.490  < 2e-16 ***
## a      36.52027    5.02663   7.265 5.63e-13 ***
## b     130.94864   16.75863   7.814 9.61e-15 ***
## c     217.30447   25.55815   8.502  < 2e-16 ***
## d       1.30810    0.11645  11.233  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5778 on 1711 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (39 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9253, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.8651, p-value = 4.49e-09
## alternative hypothesis: two.sided

predict and plot

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   2617     1396.7                                 
## 2   2616     1389.5  1   7.179 13.5148 0.0002415 ***
## 3   2520     1269.0 96 120.535  2.4933 2.212e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 28732.83
## 2     2 28721.33
## 3     3 27762.82
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      0.92778    0.90712   1.023  0.30651    
## phi     0.04066    0.01473   2.761  0.00581 ** 
## alpha   0.52784    0.05007  10.542  < 2e-16 ***
## A     170.06337   34.02318   4.998 6.18e-07 ***
## k      91.15763    7.90387  11.533  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7096 on 2520 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.741e-06
##   (96 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2520     1269.0                                
## 2   2519     1233.3  1 35.669  72.851 < 2.2e-16 ***
## 3   2519     1250.6  0  0.000                      
## 4   2518     1207.9  1 42.677  88.963 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 27762.82
## 2    3a 27692.83
## 3    3b 27727.95
## 4    3c 27642.27
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      1.02638    0.92599   1.108 0.267786    
## phi     0.04879    0.01397   3.491 0.000489 ***
## alpha   0.63236    0.03933  16.080  < 2e-16 ***
## A     130.40594   27.04390   4.822 1.51e-06 ***
## k      80.53724    5.47767  14.703  < 2e-16 ***
## p       0.18868    0.01733  10.885  < 2e-16 ***
## s       2.44328    0.29717   8.222 3.17e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6926 on 2518 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 6.271e-06
##   (96 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   2615     1381.0                                 
## 2   2614     1373.9  1   7.022 13.3599 0.0002621 ***
## 3   2518     1205.7 96 168.228  3.6596 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3c 27642.27
## 2     4 28707.13
## 3     5 28695.77
## 4     6 27637.65
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      1.04310    0.92937   1.122 0.261811    
## phi     0.04819    0.01397   3.449 0.000572 ***
## alpha   0.63571    0.03890  16.341  < 2e-16 ***
## a      24.94418    4.99508   4.994 6.33e-07 ***
## b      94.74616   19.17706   4.941 8.30e-07 ***
## c     212.83670   20.85680  10.205  < 2e-16 ***
## d       1.25548    0.10079  12.456  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.692 on 2518 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (96 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90038, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.5324, p-value = 5.832e-06
## alternative hypothesis: two.sided

predict and plot

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1753     893.12                                
## 2   1752     890.18  1  2.932  5.7696   0.01641 *  
## 3   1692     797.00 60 93.185  3.2972 1.842e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 19820.05
## 2     2 19816.27
## 3     3 19156.50
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      1.58609    1.60789   0.986  0.32406    
## phi     0.04951    0.01870   2.647  0.00819 ** 
## alpha   0.65188    0.05503  11.847  < 2e-16 ***
## A     267.34611   83.33113   3.208  0.00136 ** 
## k     164.02805   18.86160   8.696  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6863 on 1692 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 4.786e-06
##   (61 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1692     797.00                                
## 2   1691     789.13  1 7.8716  16.868 4.199e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 19156.50
## 2    3a 19141.65
## 3    3b       NA
## 4    3c       NA
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2/(k + STDAGE_t2)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      1.73215    1.69289   1.023  0.30636    
## phi     0.05386    0.01852   2.909  0.00368 ** 
## alpha   0.66456    0.05087  13.063  < 2e-16 ***
## A     329.90306  113.14657   2.916  0.00360 ** 
## k     257.91420   61.78254   4.175 3.14e-05 ***
## p       0.01881    0.00391   4.810 1.64e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6831 on 1691 degrees of freedom
## 
## Number of iterations to convergence: 45 
## Achieved convergence tolerance: 9.406e-06
##   (61 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)    
## 1   1751     828.43                              
## 2   1750     827.20  1   1.231   2.604 0.1068    
## 3   1690     713.90 60 113.295   4.470 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3a 19141.65
## 2     4 19692.03
## 3     5 19691.41
## 4     6 18973.65
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge      2.25857    1.89702   1.191  0.23398    
## phi     0.02796    0.01763   1.586  0.11296    
## alpha   0.70224    0.04134  16.985  < 2e-16 ***
## a      19.07334    6.06344   3.146  0.00169 ** 
## b      92.37563   29.34522   3.148  0.00167 ** 
## c     132.62275    5.79400  22.890  < 2e-16 ***
## d       0.96331    0.04975  19.364  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6499 on 1690 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (61 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93135, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.6964, p-value = 2.647e-06
## alternative hypothesis: two.sided

predict and plot

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    443     175.53                            
## 2    442     175.51  1  0.022  0.0548 0.81496  
## 3    345     127.57 97 47.943  1.3367 0.03139 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4440.199
## 2     2 4442.143
## 3     3 3469.759
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.407138   1.013752  -0.402 0.688216    
## phi    -0.004488   0.025349  -0.177 0.859583    
## alpha   0.782447   0.098140   7.973  2.3e-14 ***
## A     123.321200  35.167088   3.507 0.000514 ***
## k      63.554870  21.063832   3.017 0.002740 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6081 on 345 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.602e-06
##   (101 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df    Sum Sq F value Pr(>F)
## 1    345     127.57                            
## 2    344     127.57  1 0.0009742  0.0026 0.9592
## 3    344     127.56  0 0.0000000               
## 4    343     127.53  1 0.0262299  0.0705 0.7907
##   model      AIC
## 1     3 3469.759
## 2    3a 3471.757
## 3    3b 3471.734
## 4    3c 3473.662
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.407138   1.013752  -0.402 0.688216    
## phi    -0.004488   0.025349  -0.177 0.859583    
## alpha   0.782447   0.098140   7.973  2.3e-14 ***
## A     123.321200  35.167088   3.507 0.000514 ***
## k      63.554870  21.063832   3.017 0.002740 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6081 on 345 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.602e-06
##   (101 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    441     174.96                            
## 2    440     174.96  1  0.000  0.0000 1.00000  
## 3    343     127.61 97 47.344  1.3119 0.04106 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 3469.759
## 2     4 4442.739
## 3     5 4444.739
## 4     6 3473.887
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.407138   1.013752  -0.402 0.688216    
## phi    -0.004488   0.025349  -0.177 0.859583    
## alpha   0.782447   0.098140   7.973  2.3e-14 ***
## A     123.321200  35.167088   3.507 0.000514 ***
## k      63.554870  21.063832   3.017 0.002740 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6081 on 345 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 4.602e-06
##   (101 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93506, p-value = 3.149e-11
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.9043, p-value = 3.541e-09
## alternative hypothesis: two.sided

predict and plot

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    214     80.493                              
## 2    213     80.461  1 0.0328  0.0868 0.768564   
## 3    209     74.179  4 6.2812  4.4243 0.001875 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2156.928
## 2     2 2158.840
## 3     3 2125.348
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + 
##     STDAGE_t2)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.51386    0.56712  -2.669 0.008196 ** 
## phi    -0.03783    0.06907  -0.548 0.584493    
## alpha   0.52145    0.13802   3.778 0.000206 ***
## A     202.94010   57.18345   3.549 0.000478 ***
## k      88.38698   23.66402   3.735 0.000242 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5958 on 209 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 9.271e-06
##   (6 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * STDAGE_t2/(k + STDAGE_t2)
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2/(k + STDAGE_t2)))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * STDAGE_t2^s/(k^s + STDAGE_t2^s))
## Model 4: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    209     74.179                              
## 2    208     73.531  1 0.6482  1.8337 0.177163   
## 3    208     74.085  0 0.0000                    
## 4    207     70.803  1 3.2811  9.5927 0.002224 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 2125.348
## 2    3a 2125.470
## 3    3b 2127.075
## 4    3c 2119.380
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * 
##     A * STDAGE_t2^s/(k^s + STDAGE_t2^s)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.53631    0.53781  -2.857 0.004719 ** 
## phi    -0.03188    0.06598  -0.483 0.629538    
## alpha   0.56263    0.12916   4.356 2.08e-05 ***
## A     142.47922   37.97167   3.752 0.000228 ***
## k      66.69676    9.16110   7.280 6.81e-12 ***
## p       0.18019    0.03962   4.548 9.22e-06 ***
## s       3.04230    1.23140   2.471 0.014297 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5848 on 207 degrees of freedom
## 
## Number of iterations to convergence: 15 
## Achieved convergence tolerance: 5.393e-06
##   (6 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

model selection 3

## Analysis of Variance Table
## 
## Model 1: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 2: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## Model 3: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    212     76.519                              
## 2    211     76.519  1 0.0000  0.0000 1.000000   
## 3    207     70.029  4 6.4896  4.7956 0.001015 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1    3c 2119.380
## 2     4 2149.940
## 3     5 2151.940
## 4     6 2117.028
## 
## Formula: B_plt_t2_MgHa ~ (1 + (MEASTIME_t2 - 1990) * ge/100) * (1 + phi * 
##     DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t2/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.62316    0.50044  -3.243 0.001377 ** 
## phi     0.00000    0.06252   0.000 1.000000    
## alpha   0.54428    0.13036   4.175 4.38e-05 ***
## a      27.41737    7.63476   3.591 0.000411 ***
## b     116.77576   28.20651   4.140 5.05e-05 ***
## c     155.67685   22.11390   7.040 2.78e-11 ***
## d       1.03563    0.19858   5.215 4.44e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5816 on 207 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (6 observations deleted due to missingness)

summary

  • simple log-normal model: fits
  • log-normal phi model: fits
  • log-normal phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93333, p-value = 2.665e-08
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.0322, p-value = 0.302
## alternative hypothesis: two.sided

predict and plot

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod.2 Sel.Mod.3 Best.Mod
211 Northeastern Mixed Forest 3 6 6
212 Laurentian Mixed Forest 3a 6 6
221 Eastern Broadleaf Forest 3b 6 6
222 Midwest Broadleaf Forest 3b 6 6
223 Central Interior Broadleaf Forest 3b 6 6
231 Southeastern Mixed Forest 3c 6 6
232 Outer Coastal Plain Mixed Forest 3a 6 6
234 Lower Mississippi Riverine Forest 3 3 3
242 Pacific Lowland Mixed Forest NA NA NA
251 Prairie Parkland (Temperate) 3b 6 6
255 Prairie Parkland (Subtropical) 3a 6 6
261 California Coastal Chaparral Forest and Shrub NA NA NA
262 California Dry Steppe NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest 3a 3a 3a
313 Colorado Plateau Semi-Desert 3 6 6
315 Southwest Plateau and Plains Dry Steppe and Shrub NA NA NA
321 Chihuahuan Semi-Desert NA NA NA
322 American Semidesert and Desert NA NA NA
331 Great Plains/Palouse Dry Steppe 3a 3a 3a
332 Great Plains Steppe 3 6 6
341 Intermountain Semi-Desert and Desert NA NA NA
342 Intermountain Semi-Desert NA NA NA
411 Everglades NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 3b 6 6
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 3c 3c 3c
M223 Ozark Broadleaf Forest Meadow 3 3 3
M231 Ouachita Mixed Forest 3b 3b 3b
M242 Cascade Mixed Forest 3a 6 6
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 3 3 3
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow 3a 6 6
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow 3a 6 6
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 3c 6 6
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 3a 6 6
M334 Black Hills Coniferous Forest 3 3 3
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow 3c 6 6

table by ecoprovince

Code Ecoregion region n.obs n.plots ge ge.variance ge.2.5 ge.97.5 phi phi.variance phi.2.5 phi.97.5 alpha alpha.variance alpha.2.5 alpha.97.5 A A.2.5 A.97.5 k k.2.5 k.97.5 a a.2.5 a.97.5 b b.se b.2.5 b.97.5 c c.2.5 c.97.5 d d.2.5 d.97.5
211 Northeastern Mixed Forest east 6884 2879 0.8813298 0.0385461 0.4964587 1.2662009 0.0000000 0.0000166 -0.0079834 0.0079834 0.8426527 0.0007101 0.7904150 0.8948904 387.2824 339.80547 434.7593 170.93933 1.482754e+02 193.60327 37.964963 34.6005556 41.32937 102.86037 NA 93.69637 112.02437 114.69626 106.42497 122.96755 0.9253480 0.8481489 1.0025471
212 Laurentian Mixed Forest east 22685 9493 0.4140232 0.0135036 0.1862505 0.6417958 0.0079614 0.0000077 0.0025056 0.0134171 0.7834429 0.0002186 0.7544657 0.8124202 230.0844 208.94713 251.2217 122.01600 1.050630e+02 138.96896 23.935105 22.5724057 25.29780 80.31661 NA 76.05026 84.58296 109.65272 103.79840 115.50703 1.1955780 1.1383684 1.2527877
221 Eastern Broadleaf Forest east 7307 3560 0.1820948 0.0151020 -0.0588062 0.4229959 0.0000000 0.0000113 -0.0065768 0.0065768 0.8234610 0.0006287 0.7743096 0.8726124 328.1596 279.12094 377.1982 75.60570 5.893544e+01 92.27596 30.305358 26.2700899 34.34063 165.27209 NA 150.56033 179.98385 136.54946 118.54115 154.55777 1.3442416 1.2204524 1.4680308
222 Midwest Broadleaf Forest east 5846 2589 -0.1604805 0.0364924 -0.5349856 0.2140247 0.0293096 0.0000649 0.0135116 0.0451077 0.8611978 0.0012151 0.7928601 0.9295355 254.4786 204.21299 304.7443 74.31014 5.401579e+01 94.60449 26.981911 23.8644488 30.09937 117.43133 NA 106.63587 128.22678 102.33991 93.72365 110.95617 1.0169469 0.9281184 1.1057755
223 Central Interior Broadleaf Forest east 10006 3860 0.1196577 0.0124990 -0.0994946 0.3388099 0.0000000 0.0000176 -0.0082323 0.0082323 0.7696807 0.0006790 0.7186006 0.8207608 173.7654 157.98769 189.5431 40.14399 3.515267e+01 45.13530 31.403491 27.5825784 35.22440 103.16963 NA 96.31482 110.02444 102.24776 94.39256 110.10295 1.2127052 1.1106756 1.3147348
231 Southeastern Mixed Forest east 12844 5935 2.1217165 0.0355755 1.7520030 2.4914300 0.0000000 0.0000134 -0.0071633 0.0071633 0.8065997 0.0001042 0.7865876 0.8266117 126.5825 117.51179 135.6532 32.08316 3.036956e+01 33.79675 26.098675 24.5400334 27.65732 97.84423 NA 90.20193 105.48654 101.68725 90.77491 112.59959 1.3833389 1.2911898 1.4754880
232 Outer Coastal Plain Mixed Forest east 13167 6463 1.3225831 0.0321247 0.9712581 1.6739081 0.0223844 0.0000178 0.0141249 0.0306439 0.8716493 0.0000685 0.8554209 0.8878777 685.0304 431.48304 938.5778 384.89604 2.116345e+02 558.15754 32.786968 30.6808067 34.89313 104.58378 NA 95.18145 113.98612 106.22272 92.62807 119.81737 1.3231333 1.2164743 1.4297923
234 Lower Mississippi Riverine Forest east 1344 759 0.0553654 0.1712485 -0.7564800 0.8672107 0.0217006 0.0002104 -0.0067569 0.0501580 0.6620878 0.0029326 0.5558480 0.7683275 550.8414 366.92569 734.7570 164.62568 1.030939e+02 226.15747 NA NA NA NA NA NA NA NA NA NA NA NA NA
242 Pacific Lowland Mixed Forest pacific 85 85 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
251 Prairie Parkland (Temperate) east 2290 903 0.3166112 0.0992728 -0.3013470 0.9345694 0.0000000 0.0000700 -0.0164080 0.0164080 0.7210026 0.0043343 0.5918790 0.8501261 145.0376 118.32125 171.7540 38.92230 3.202015e+01 45.82444 26.749847 19.1336653 34.36603 93.30996 NA 78.42397 108.19596 99.58963 86.01890 113.16036 1.0975156 0.9137136 1.2813176
255 Prairie Parkland (Subtropical) east 714 318 -0.1859521 0.1765241 -1.0109372 0.6390330 0.0000000 0.0002155 -0.0288221 0.0288221 0.6430370 0.0060449 0.4903726 0.7957013 266.5110 97.32554 435.6964 119.97203 5.086584e+00 234.85747 22.558489 16.9617842 28.15519 75.97870 NA 59.18193 92.77547 59.50946 48.79835 70.22057 0.9985524 0.7736257 1.2234791
261 California Coastal Chaparral Forest and Shrub pacific 26 26 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 159 157 -0.0777708 1.6428227 -2.6104792 2.4549376 -0.0271234 0.0044972 -0.1596371 0.1053903 0.8592773 0.0576453 0.3848478 1.3337067 19316.5492 -21300.54714 59933.6456 4915.53636 -6.143886e+03 15974.95866 NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert interior west 218 218 -1.2871343 0.4558669 -2.6182059 0.0439372 0.0322690 0.0012367 -0.0370586 0.1015966 0.2997387 0.0606681 -0.1858431 0.7853205 258.0581 55.41657 460.6996 135.22109 2.508344e+01 245.35873 53.322071 21.1701179 85.47402 144.62680 NA 61.50967 227.74393 139.92344 125.13669 154.71018 0.5729363 0.4034699 0.7424026
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 4 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 9 9 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 3 3 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 331 255 0.7225403 3.0496758 -2.7137545 4.1588352 -0.0887580 0.0004285 -0.1294900 -0.0480260 0.8582539 0.0139587 0.6257737 1.0907341 100.8624 -27.36391 229.0887 119.62952 -1.404501e+02 379.70913 NA NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe interior west 232 128 1.1813563 5.1924335 -3.3135787 5.6762913 0.0000000 0.0010189 -0.0629659 0.0629659 0.8182331 0.0575269 0.3451107 1.2913554 385.2574 -379.78999 1150.3048 276.62580 -3.178168e+02 871.06845 25.785272 0.9302398 50.64030 77.36146 NA -52.28485 207.00776 143.44351 -160.29543 447.18245 1.0826067 -0.3909927 2.5562062
341 Intermountain Semi-Desert and Desert interior west 66 64 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert interior west 124 123 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
411 Everglades east 96 63 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 6778 3008 0.6752105 0.0252576 0.3636647 0.9867562 0.0161825 0.0000124 0.0092833 0.0230816 0.8210021 0.0004796 0.7780697 0.8639346 237.6527 206.30929 268.9961 73.75687 5.982324e+01 87.69050 16.530726 11.2043078 21.85714 148.22719 NA 128.25566 168.19872 199.46105 151.93778 246.98431 1.6450846 1.4322431 1.8579262
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 8186 3765 1.3577291 0.0229653 1.0606656 1.6547926 -0.0314710 0.0000118 -0.0382038 -0.0247381 0.8452651 0.0008947 0.7866320 0.9038982 148.4893 139.66858 157.3100 38.36194 3.679689e+01 39.92699 NA NA NA NA NA NA NA NA NA NA NA NA NA
M223 Ozark Broadleaf Forest Meadow east 893 348 -0.4816973 0.0485101 -0.9139735 -0.0494211 0.0566491 0.0001773 0.0305163 0.0827820 0.8803414 0.0052175 0.7385740 1.0221089 307.3827 240.51824 374.2472 92.08986 6.417436e+01 120.00535 NA NA NA NA NA NA NA NA NA NA NA NA NA
M231 Ouachita Mixed Forest east 1009 496 0.5442074 0.2614686 -0.4592286 1.5476434 0.0034292 0.0002162 -0.0254238 0.0322823 0.7387797 0.0040838 0.6133752 0.8641841 6025.0050 -158038.39151 170088.4016 22220.86563 -8.897138e+05 934155.54195 NA NA NA NA NA NA NA NA NA NA NA NA NA
M242 Cascade Mixed Forest pacific 3303 3286 -0.2724529 0.2214455 -1.1951194 0.6502136 0.0000000 0.0002309 -0.0297909 0.0297909 1.0848472 0.0046031 0.9518213 1.2178730 886.8631 629.63517 1144.0910 183.45392 1.405151e+02 226.39275 8.656743 -12.2623717 29.57586 568.18302 NA 400.23976 736.12627 556.00850 344.86803 767.14898 2.0364456 1.7044233 2.3684679
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 1993 1828 -1.1584426 0.1093862 -1.8071353 -0.5097499 0.2025361 0.0001710 0.1768858 0.2281863 0.7555371 0.0103421 0.5560744 0.9549997 858.6293 629.19423 1088.0644 131.30793 9.833949e+01 164.27638 NA NA NA NA NA NA NA NA NA NA NA NA NA
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 30 26 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 367 367 -1.6468449 0.1214047 -2.4287938 -0.8648960 0.0494208 0.0004801 0.0063297 0.0925119 0.5827595 0.0172642 0.3243598 0.8411592 1053.4901 -785.59435 2892.5746 553.32368 -6.503688e+02 1757.01616 49.309457 23.9042394 74.71467 182.53573 NA 96.28308 268.78837 174.61256 99.67213 249.55299 0.9532734 0.5604644 1.3460824
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 1757 1757 -0.8839650 0.1128560 -1.5428624 -0.2250677 0.0272120 0.0001164 0.0060536 0.0483704 0.6419474 0.0015156 0.5655916 0.7183033 338.8970 224.01171 453.7822 209.27405 1.175344e+02 301.01371 36.520268 26.6612796 46.37926 130.94864 NA 98.07908 163.81820 217.30447 167.17596 267.43298 1.3081017 1.0797090 1.5364944
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 2621 2611 1.0431021 0.8637332 -0.7793105 2.8655147 0.0481868 0.0001952 0.0207895 0.0755841 0.6357063 0.0015134 0.5594212 0.7119914 130.4059 77.37537 183.4365 80.53724 6.979605e+01 91.27844 24.944176 15.1493007 34.73905 94.74616 NA 57.14173 132.35059 212.83670 171.93847 253.73493 1.2554814 1.0578418 1.4531210
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 1758 1747 2.2585657 3.5986739 -1.4621843 5.9793156 0.0279551 0.0003107 -0.0066193 0.0625294 0.7022357 0.0017093 0.6211452 0.7833262 329.9031 107.98100 551.8251 257.91420 1.367359e+02 379.09250 19.073342 7.1806968 30.96599 92.37563 NA 34.81883 149.93243 132.62275 121.25858 143.98692 0.9633133 0.8657379 1.0608888
M334 Black Hills Coniferous Forest interior west 451 179 -0.4071378 1.0276930 -2.4010500 1.5867743 -0.0044877 0.0006426 -0.0543455 0.0453701 0.7824467 0.0096315 0.5894184 0.9754750 123.3212 54.15232 192.4901 63.55487 2.212518e+01 104.98456 NA NA NA NA NA NA NA NA NA NA NA NA NA
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 220 220 -1.6231596 0.2504413 -2.6097745 -0.6365448 0.0000000 0.0039085 -0.1232539 0.1232539 0.5442843 0.0169925 0.2872899 0.8012788 142.4792 67.61844 217.3400 66.69676 4.863574e+01 84.75777 27.417368 12.3655141 42.46922 116.77576 NA 61.16691 172.38462 155.67685 112.07951 199.27419 1.0356338 0.6441368 1.4271308

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I

plot phi (effect of DeltaPDSI)

plot alpha (biomass compensation effect)

plot A (asymptote of B)

## Warning: Removed 12 rows containing missing values (geom_point).

plot k (stand age at half biomass asymptote)

## Warning: Removed 12 rows containing missing values (geom_point).

Caclulations - weighted averages

ge (stand biomass enhancement factor in % 2000-2021)

##          region weighted.ge weighted.ge.std_Error 95 % CI, upper 95 % CI, lower
## 1     entire US  0.64186955            0.08855911     0.81544540     0.46829370
## 2       pacific -0.05258158            0.02907018     0.00439597    -0.10955912
## 3          east  0.62254977            0.04104178     0.70299165     0.54210789
## 4 interior west  0.07190135            0.07289179     0.21476926    -0.07096656

phi (effect of DeltaPDSI)

##          region weighted.phi weighted.phi.std_Error 95 % CI, upper
## 1     entire US  0.014850562           2.965367e-08    0.014850620
## 2       pacific  0.006361287           9.794231e-04    0.008280956
## 3          east  0.004592308           1.019822e-03    0.006591159
## 4 interior west  0.003896967           9.545942e-04    0.005767971
##   95 % CI, lower
## 1    0.014850504
## 2    0.004441617
## 3    0.002593458
## 4    0.002025962

alpha (biomass compensation effect)

##          region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1     entire US     0.80054289             1.340699e-07     0.80054315
## 2       pacific     0.08831322             5.087893e-03     0.09828549
## 3          east     0.62745699             5.002736e-03     0.63726236
## 4 interior west     0.08477267             2.929348e-03     0.09051420
##   95 % CI, lower
## 1     0.80054263
## 2     0.07834095
## 3     0.61765163
## 4     0.07903115

A (asymptote of forest biomass in Mg/ha)

##          region weighted.A
## 1     entire US   444.6020
## 2       pacific  1396.6006
## 3          east   359.5654
## 4 interior west     0.0000

K (stand age at half maturation in years)

##          region weighted.k
## 1     entire US   339.4760
## 2       pacific   299.9999
## 3          east   372.7147
## 4 interior west   175.4720

Model Bookeeping

1. Delta-B due to Delta-STDAGE

2. Delta-B due to Delta-Year (ge)

make a fig

## Warning: Removed 16224 rows containing missing values (geom_point).

3. stand age densities

make a fig

## Warning: package 'ggridges' was built under R version 4.2.2
## Picking joint bandwidth of 7.36